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example_polytopetools.py.out
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example_polytopetools.py.out
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The polytope tools in BurnMan can be used to calculate all potential endmembers in a solid solution.
Endmember occupancies for bridgmanite in the FMASO system
([Mg,Fe,Fe3+,Al3+][Fe3+,Al3+,Si]O3)
Each of the following lines represents a distinct endmember:
[[1. 0. 0. 0. 0. 0. 1.]
[0. 1. 0. 0. 0. 0. 1.]
[0. 0. 1. 0. 0. 1. 0.]
[0. 0. 1. 0. 1. 0. 0.]
[0. 0. 0. 1. 1. 0. 0.]
[0. 0. 0. 1. 0. 1. 0.]]
Endmember formulae corresponding to these occupancies:
['[Mg][Si]', '[Fe][Si]', '[Fef][Al]', '[Fef][Fef]', '[Al][Fef]', '[Al][Al]']
Endmember occupancies for two-site pyrope-majorite
(i.e. Mg3[Mg,Al,Si][Mg,Al,Si]Si3O12)
Each of the following lines represents a distinct endmember:
[[1. 0. 0. 0. 0. 1. ]
[0.5 0. 0.5 0. 1. 0. ]
[0. 1. 0. 0.5 0. 0.5]
[0. 1. 0. 0. 1. 0. ]
[0. 0. 1. 1. 0. 0. ]]
A potential set of independent endmember site occupancies:
[[1. 0. 0. 0. 0. 1. ]
[0.5 0. 0.5 0. 1. 0. ]
[0. 1. 0. 0.5 0. 0.5]
[0. 1. 0. 0. 1. 0. ]]
Formulae corresponding to these independent endmember occupancies:
['[Mg][Si]', '[Mg1/2Si1/2][Al]', '[Al][Mg1/2Si1/2]', '[Al][Al]']
The complete set of endmembers expressed as proportions of the independent endmember set:
[[ 1. -0. -0. -0.]
[ 0. 1. -0. 0.]
[-0. 0. 1. -0.]
[-0. 0. 0. 1.]
[-1. 2. 2. -2.]]
We can also create a polytope using the site-species occupancies of a set of independent endmembers of a solution. Here we do this for the garnet solid solution provided in the Stixrude and Lithgow-Bertelloni database.
Endmember compositions:
Mg3Al2Si3O12
Fe3Al2Si3O12
Ca3Al2Si3O12
Mg4Si4O12
Na2Al2Si4O12
Endmembers as independent endmember amounts:
[[-0. -0. -0. 1. 0.]
[ 1. 0. 0. 0. 0.]
[ 0. 1. 0. -0. -0.]
[-1. 1. 0. 1. -0.]
[ 0. 0. 1. -0. 0.]
[-1. -0. 1. 1. 0.]
[ 0. -0. -0. 0. 1.]]
Site occupancies for all endmembers:
[Mg]3[Mg][Si]
[Mg]3[Al][Al]
[Fe]3[Al][Al]
[Fe]3[Mg][Si]
[Ca]3[Al][Al]
[Ca]3[Mg][Si]
[Na2/3Al1/3]3[Al][Si]
Composites are also constrained by linear equalities and inequalities. Here, we demonstrate how BurnMan can take a composite and a bulk composition, and simplify the composite so that it only contains endmembers which can have non-zero quantities.
The starting assemblage includes NCFMAS garnet and FMS olivine.
Starting composition: Mg18Fe2Si15O50
The simplifying function has returned a modified assemblage.
The old assemblage included endmembers with the following compositions:
['Mg3Al2Si3O12', 'Fe3Al2Si3O12', 'Ca3Al2Si3O12', 'Mg4Si4O12', 'Na2Al2Si4O12', 'Mg2SiO4', 'Fe2SiO4']
Which led to the following extreme vertices satifying the bulk compositional constraints:
[[-2/3 2/3 0 5/2 0 5 0]
[0 0 0 5/2 0 4 1]]
The new assemblage has fewer endmembers, with compositions:
['Mg4Si4O12', 'MgFe3Si4O12', 'Mg2SiO4', 'Fe2SiO4']
The same vertices now look like this:
[[11/6 2/3 5 0]
[5/2 0 4 1]]